Fast methods, which aim to improve the time-efficiency of NMR data acquisition have been pioneered since the early days of multidimensional NMR. Many of these methods aim to record a subset of the fully-sampled data matrix, thus reducing the time required to sample the indirect dimensions. This allows improvements in resolution, sensitivity or reductions in experiment time, or a combination of all three. Such an approach to sampling the indirect dimensions is known as non-uniform sampling, sparse sampling or undersampling. Associated with non-uniform sampling is a collection of reconstruction methods which aim to reconstruct the full data set, or the information contained in the spectrum from the undersampled raw data. Some methods have very specific requirements as to the data sampling, for example projections taken through the data, whilst other methods are less prescriptive on the data sampling requirements, although some sampling patterns may give preferential results.
Compressed sensing was pioneered in the field of information theory and is popular in an number of fields including MRI. Compressed sensing provides theoretical guarantees as to the reconstruction quality obtainable from an undersampled data set. CS has been proven to be a powerful tool for reconstructing undersampled NMR spectra across a wide range of experiment types. Various software packages are available to carry out CS reconstructions, including our own, Cambridge CS. In the following pages, we give some general guidelines for CS reconstructions of NMR data, as well as more specific details relevant to the Cambridge CS software.